β-Ga2O3 single-crystal substrate

ABSTRACT

A β-Ga2O3-based single-crystal substrate includes a β-Ga2O3-based single crystal, and a principal surface being a plane parallel to a b-axis of the β-Ga2O3-based single crystal. A maximum value of Δω on an arbitrary straight line on the principal surface that passes through a center of the principal surface is not more than 0.7264. The Δω is a difference between a maximum value and a minimum value of values obtained by subtracting ωa from ωs at each of measurement positions, where ωs represents an angle defined by an X-ray incident direction and the principal surface at a peak position of an X-ray rocking curve on the straight line and ωa represents an angle on an approximated straight line obtained by using least-squares method to linearly approximate a curve representing a relationship between the ωs and the measurement positions thereof.

TECHNICAL FIELD

The invention relates to a β-Ga₂O₃-based single-crystal substrate.

BACKGROUND ART

Use of EFG (Edge-defined Film-fed Growth) technique to grow aflat-plate-shaped Ga₂O₃ single crystal is known as a conventional method(see, e.g., PTL 1).

In PTL 1, SiO₂ is used as a dopant material to introduce Si into a Ga₂O₃single crystal. Since SiO₂ has a small melting point difference from theGa₂O₃ and has a low vapor pressure at a growth temperature of the Ga₂O₃single crystal (at a melting point of a raw material of the Ga₂O₃ singlecrystal), it is easy to control the amount of dopant in the Ga₂O₃ singlecrystal.

Meanwhile, use of FZ (Floating Zone) technique to grow a column-shapedβ-Ga₂O₃-based single crystal is also known as a conventional method(see, e.g., PTL 2).

In PTL 2, Si, Sn, Zr, Hf or Ge, etc., used as a thermally meltablecontrol additive are added to a β-Ga₂O₃-based single crystal. Additionof the thermally meltable control additive increases infrared absorptionproperties of the β-Ga₂O₃-based single crystal and causes theβ-Ga₂O₃-based single crystal to efficiently absorb infrared light from alight source of a FZ apparatus. Thus, even in a β-Ga₂O₃-based singlecrystal having a large outer diameter, a temperature difference betweenthe center portion and the outer portion is reduced and the centerportion is not solidified easily.

CITATION LIST Patent Literature

[PTL 1]

JP-A-2011-190127

[PTL 2]

JP-A-2006-273684

SUMMARY OF INVENTION Technical Problem

It is an object of the invention to provide a high-quality β-Ga₂O₃-basedsingle-crystal substrate that has little variation in crystal structure.

Solution to Problem

According to an embodiment of the invention, in order to attain theobject, a β-Ga₂O₃-based single-crystal substrate defined by [1] to [10]below is provided.

[1] A β-Ga₂O₃-based single-crystal substrate, comprising:

-   -   a β-Ga₂O₃-based single crystal; and    -   a principal surface being a plane parallel to a b-axis of the        β-Ga₂O₃-based single crystal,    -   wherein a maximum value of Δω on an arbitrary straight line on        the principal surface that passes through a center of the        principal surface is not more than 0.7264, and    -   wherein the Δω is a difference between a maximum value and a        minimum value of values obtained by subtracting ω_(a) from ω_(s)        at each of measurement positions, where ω_(s) represents an        angle defined by an X-ray incident direction and the principal        surface at a peak position of an X-ray rocking curve on the        straight line and ω_(a) represents an angle on an approximated        straight line obtained by using least-squares method to linearly        approximate a curve representing a relationship between the        ω_(s) and the measurement positions thereof.

[2] A β-Ga₂O₃-based single-crystal substrate, comprising:

-   -   a β-Ga₂O₃-based single crystal; and    -   a principal surface being a plane parallel to a b-axis of the        β-Ga₂O₃-based single crystal,    -   wherein a maximum value of α on an arbitrary straight line on        the principal surface that passes through a center of the        principal surface is not more than 0.141, and    -   wherein the α is an average value of absolute values obtained by        subtracting ω_(a) from ω_(s) at each of measurement positions,        where ω_(s) represents an angle defined by an X-ray incident        direction and the principal surface at a peak position of an        X-ray rocking curve on the straight line and ω_(a) represents an        angle on an approximated straight line obtained by using        least-squares method to linearly approximate a curve        representing a relationship between the ω_(s) and the        measurement positions thereof.

[3] The β-Ga₂O₃-based single-crystal substrate according to [1], whereinΔω on a straight line perpendicular to the b-axis of the β-Ga₂O₃-basedsingle crystal is a maximum among the Δω on the arbitrary straight line.

[4] The β-Ga₂O₃-based single-crystal substrate according to [2], whereinα on a straight line perpendicular to the b-axis of the β-Ga₂O₃-basedsingle crystal is a maximum among the α on the arbitrary straight line.

[5] The β-Ga₂O₃-based single-crystal substrate according to any one of[1] to [4], comprising a dopant.

[6] The β-Ga₂O₃-based single-crystal substrate according to [5], whereinthe dopant is a Group IV element.

[7] The β-Ga₂O₃-based single-crystal substrate according to [6], whereinthe dopant is Sn or Si.

[8] The β-Ga₂O₃-based single-crystal substrate according to any one of[1] to [7], wherein the principal surface is a (−201) plane, a (101)plane or a (001) plane.

[9] The β-Ga₂O₃-based single-crystal substrate according to any one of[1] to [8], wherein the substrate is cut out from a flat-plate-shapedβ-Ga₂O₃-based single crystal grown in the b-axis direction.

[10] The β-Ga₂O₃-based single-crystal substrate according to any one of[1] to [9], wherein the substrate comprises no twinning plane or aregion that does not include a twinning plane that is not less than 2inches in a maximum width in a direction perpendicular to anintersection line between the twinning plane and the principal surface.

Advantageous Effects of Invention

According to the invention, a high-quality β-Ga₂O₃-based single-crystalsubstrate that has little variation in crystal structure can beprovided.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a vertical cross-sectional view showing an EFG crystalmanufacturing apparatus in a first embodiment.

FIG. 2 is a perspective view showing a state during growth of aβ-Ga₂O₃-based single crystal in the first embodiment.

FIG. 3 is a perspective view showing a state of growing a β-Ga₂O₃-basedsingle crystal to be cut into a seed crystal.

FIG. 4 is plan view showing a β-Ga₂O₃-based single-crystal substrate cutout from the β-Ga₂O₃-based single crystal and X-ray diffractionmeasurement positions thereon.

FIG. 5 is a schematic diagram illustrating a state during X-ray rockingcurve measurement.

FIG. 6A is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

FIG. 6B is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

FIG. 6C is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

FIG. 7A is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

FIG. 7B is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

FIG. 7C is a graph showing a curved line representing a relation betweena measurement position on the substrate and ω_(r) as a value of ω at anX-ray rocking curve peak position and also showing an approximation linethereof obtained by linear approximation using the least squares method.

DESCRIPTION OF EMBODIMENT Embodiment Summary of Embodiment

In the present embodiments, a plate-shaped β-Ga₂O₃-based single crystalis grown from a seed crystal. It is possible to reduce variation incrystal structure by using the growth method described later to grow theplate-shaped β-Ga₂O₃-based single crystal.

Variation in crystal structure of β-Ga₂O₃-based single crystal has apeak along a direction perpendicular to the b-axis direction. Thus, inthe present embodiment, variation in crystal structure of aβ-Ga₂O₃-based single-crystal substrate cut out from a plate-shapedβ-Ga₂O₃-based single crystal is used as an evaluation indicator and ismeasured in a direction parallel to the principal surface as well asperpendicular to the b-axis direction.

(Method of Manufacturing β-Ga₂O₃-Based Single-Crystal Substrate)

A method of manufacturing a β-Ga₂O₃-based single-crystal substrate 1having little variation in crystal structure will be described below asan example.

FIG. 1 is a vertical cross-sectional view showing an EFG (Edge DefinedFilm Fed Growth) crystal manufacturing apparatus 10 in the firstembodiment.

The EFG crystal manufacturing apparatus 10 has a crucible 11 which isplaced in a quartz tube 18 and contains Ga₂O₃-based melt 30, a die 12placed in the crucible 11 and having a slit 12 a, a lid 13 covering anopening of the crucible 11 so that the top surface of the die 12including an opening 12 b is exposed, a seed crystal holder 14 forholding a seed crystal 31, a shaft 15 vertically movably supporting theseed crystal holder 14, a support base 16 for placing the crucible 11, aheat insulator 17 provided along an inner wall of the quartz tube 18, ahigh-frequency coil 19 for high-frequency induction heating providedaround the quartz tube 18, a base 22 for supporting the quartz tube 18and the heat insulator 17, and leg portions 23 attached to the base 22.

The EFG crystal manufacturing apparatus 10 further includes anafter-heater 20 and a reflective plate 21. The after-heater 20 is formedof Ir, etc., and is provided to surround a region above the crucible 11where a β-Ga₂O₃-based single crystal 32 is grown. The reflective plate21 is formed of Ir, etc., and is provided, like a lid, on theafter-heater 20.

The crucible 11 contains the Ga₂O₃-based melt 30 which is obtained bymelting a Ga₂O₃-based raw material. The crucible 11 is formed of ahighly heat-resistant material such as Ir capable of containing theGa₂O₃-based melt 30.

The die 12 has the slit 12 a to draw up the Ga₂O₃-based melt 30 in thecrucible 11 by capillary action. The die 12 is formed of a highlyheat-resistant material such as Ir in the same manner as the crucible11.

The lid 13 prevents the high-temperature Ga₂O₃-based melt 30 fromevaporating from the crucible 11 and further prevents the evaporatedsubstances from attaching to members located outside of the crucible 11.

The high-frequency coil 19 is helically arranged around the quartz tube18 and inductively heats the crucible 11 and the after-heater 20 by ahigh-frequency current which is supplied from a non-illustrated powersource. This causes the Ga₂O₃-based raw material in the crucible to meltand the Ga₂O₃-based melt 30 is thereby obtained.

The heat insulator 17 is provided around the crucible 11 with apredetermined gap. The heat insulator 17 retains heat and is thuscapable of suppressing a rapid temperature change of theinductively-heated crucible 11, etc.

The after-heater 20 generates heat by induction heating and thereflective plate 21 downwardly reflects heat radiated from theafter-heater 20 and the crucible 11. The present inventors confirmedthat the after-heater 20 is capable of reducing radial (horizontal)temperature gradient in a hot zone and the reflective plate 21 iscapable of reducing temperature gradient in a crystal growth directionin the hot zone.

It is possible to reduce dislocation density of the β-Ga₂O₃-based singlecrystal 32 by providing the after-heater 20 and the reflective plate 21on the EFG crystal manufacturing apparatus 10. This allows theβ-Ga₂O₃-based single-crystal substrate 1 having little variation incrystal structure to be obtained from the β-Ga₂O₃-based single crystal32.

FIG. 2 is a perspective view showing a state during growth of theβ-Ga₂O₃-based single crystal 32 in the first embodiment. Illustrationsof members around the β-Ga₂O₃-based single crystal 32 are omitted inFIG. 2.

To grow the β-Ga₂O₃-based single crystal 32, firstly, the Ga₂O₃-basedmelt 30 in the crucible 11 is drawn up to the opening 12 b of the die 12through the slit 12 a of the die 12, and the seed crystal 31 is thenbrought into contact with the Ga₂O₃-based melt 30 present in the opening12 b of the die 12. Next, the seed crystal 31 in contact with theGa₂O₃-based melt 30 is pulled vertically upward, thereby growing theβ-Ga₂O₃-based single crystal 32. The crystal growth direction shown inFIG. 2 is a direction parallel to the b-axis of the β-Ga₂O₃-based singlecrystal 32 (the b-axis direction).

The β-Ga₂O₃-based single crystal 32 and the seed crystal 31 are β-Ga₂O₃single crystals, or Ga₂O₃ single crystals doped with an element such asAl or In, and may be, e.g., a (Ga_(x)Al_(y)In_((1-x-y)))₂O₃ (0<x≤1,0≤y≤1, 0<x+y≤1) single crystal which is a β-Ga₂O₃ single crystal dopedwith Al and In. The band gap is widened by adding Al and is narrowed byadding In. The β-Ga₂O₃-based single crystal 32 may also contain anelement, e.g., Mg, Fe, Cu, Ag, Zn, Cd, Al, In, Si, Ge, Sn, Pb or Nb,etc., as a dopant.

The seed crystal 31 is a β-Ga₂O₃-based single crystal which does nothave or hardly has twinning planes. The seed crystal 31 hassubstantially the same width and thickness as the β-Ga₂O₃-based singlecrystal 32 to be grown. Thus, it is possible to grow the β-Ga₂O₃-basedsingle crystal 32 without broadening a shoulder thereof in a widthdirection W and a thickness direction T.

Since the growth of the β-Ga₂O₃-based single crystal 32 does not involvea process of broadening a shoulder in the width direction W, twinning ofthe β-Ga₂O₃-based single crystal 32 is suppressed. Meanwhile, unlike thebroadening of shoulder in the width direction W, twins are less likelyto be formed when broadening the shoulder in the thickness direction T,and thus the growth of the β-Ga₂O₃-based single crystal 32 may involve aprocess of broadening a shoulder in the thickness direction T. However,in the case that the process of broadening a shoulder in the thicknessdirection T is not performed, substantially the entire β-Ga₂O₃-basedsingle crystal 32 becomes a plate-shaped region which can be cut intosubstrates and this allows the substrate manufacturing cost to bereduced. Therefore, it is preferable to not perform the process ofbroadening a shoulder in the thickness direction T but to use a thickseed crystal 31 to ensure sufficient thickness of the β-Ga₂O₃-basedsingle crystal 32 as shown in FIG. 2.

The plane orientation of a horizontally-facing surface 33 of the seedcrystal 31 coincides with that of a principal surface 34 of theβ-Ga₂O₃-based single crystal 32. Therefore, for obtaining theβ-Ga₂O₃-based single-crystal substrate 1 having, e.g., the(−201)-oriented principal surface from the β-Ga₂O₃-based single crystal32, the β-Ga₂O₃-based single crystal 32 is grown in a state that thesurface 33 of the seed crystal 31 is oriented to (−201).

The β-Ga₂O₃-based single crystal has high cleavability on the (100)plane, and twins with the (100) plane as a twinning plane (a plane ofsymmetry) are likely to be formed in the shoulder broadening processduring crystal growth. The b-axis direction, which is the crystal growthdirection of the β-Ga₂O₃-based single crystal 32 in the presentembodiment, is parallel to the (100) plane. Therefore, even if twins areformed, it is still possible to cut out a relatively large β-Ga₂O₃-basedsingle-crystal substrate of, e.g., not less than 2 inches which does notcontain twins. It is also possible to cut out a β-Ga₂O₃-basedsingle-crystal substrate having a region which has a maximum width ofnot less than 2 inches in a direction perpendicular to a line ofintersection between a twinning plane and the principal surface and doesnot contain twinning planes.

Next, a method in which a wide seed crystal 31 with a width equivalentto the β-Ga₂O₃-based single crystal 32 is formed using a quadrangularprism-shaped narrow-width seed crystal will be described.

FIG. 3 is a perspective view showing a state of growing β-Ga₂O₃-basedsingle crystal 36 to be cut into the seed crystal 31.

The seed crystal 31 is cut from a region of the β-Ga₂O₃-based singlecrystal 36 not having or hardly having twinning planes. Therefore, awidth (a size in the width direction W) of the β-Ga₂O₃-based singlecrystal 36 is larger than the width of the seed crystal 31.

Meanwhile, a thickness (a size in the thickness direction T) of theβ-Ga₂O₃-based single crystal 36 may be smaller than the thickness of theseed crystal 31. In such a case, the seed crystal 31 is not cut directlyfrom the β-Ga₂O₃-based single crystal 36. Instead, a β-Ga₂O₃-basedsingle crystal is firstly grown from a seed crystal cut from theβ-Ga₂O₃-based single crystal 36 while broadening a shoulder in thethickness direction T and is then cut into the seed crystal 31.

For growing the β-Ga₂O₃-based single crystal 36, it is possible to usean EFG crystal manufacturing apparatus 100 which has substantially thesame structure as the EFG crystal manufacturing apparatus 10 used forgrowing the β-Ga₂O₃-based single crystal 32. However, width, or widthand thickness, of a die 112 of the EFG crystal manufacturing apparatus100 is/are different from that/those of the die 12 of the EFG crystalmanufacturing apparatus 10 since the width, or width and thickness, ofthe β-Ga₂O₃-based single crystal 36 is/are different from that/those ofthe β-Ga₂O₃-based single crystal 32. The size of an opening 112 b of thedie 112 is generally the same as the opening 12 b of the die 12 but maynot be the same.

A seed crystal 35 is a quadrangular prism-shaped β-Ga₂O₃-based singlecrystal with a smaller width than the β-Ga₂O₃-based single crystal 36 tobe grown.

To grow the β-Ga₂O₃-based single crystal 36, firstly, the Ga₂O₃-basedmelt 30 in the crucible 11 is drawn up to the opening 112 b of the die112 through a slit of the die 112, and the seed crystal 35 is thenbrought into contact with the Ga₂O₃-based melt 30 present in the opening112 b of the die 112 in a state that a horizontal position of the seedcrystal 35 is offset in the width direction W from the center of the die12 in the width direction W. In this regard, more preferably, the seedcrystal 35 is brought into contact with the Ga₂O₃-based melt 30 coveringthe top surface of the die 112 in a state that the horizontal positionof the seed crystal 35 is located above an edge of the die 112 in thewidth direction W.

Next, the seed crystal 35 in contact with the Ga₂O₃-based melt 30 ispulled vertically upward, thereby growing the β-Ga₂O₃-based singlecrystal 36.

In case that the growing β-Ga₂O₃-based single crystal is twinned duringthe process of broadening a shoulder in a width direction, twinningplanes are likely to be formed in a region close to the seed crystal andare less likely to be formed at positions distant from the seed crystal.

The method of growing the β-Ga₂O₃-based single crystal 36 in the presentembodiment uses such twinning properties of the β-Ga₂O₃-based singlecrystal. In the present embodiment, since the β-Ga₂O₃-based singlecrystal 36 is grown in the state that the horizontal position of theseed crystal 35 is offset in the width direction W from the center ofthe die 12 in the width direction W, a region far from the seed crystal35 is large in the β-Ga₂O₃-based single crystal 36, as compared to thecase of growing the β-Ga₂O₃-based single crystal 36 in a state that thehorizontal position of the seed crystal 35 is located on the center ofthe die 12 in the width direction W. Twinning planes are less likely tobe formed in such a region and it is thus possible to cut out a wideseed crystal 31.

For growing the β-Ga₂O₃-based single crystal 36 using the seed crystal35 and for cutting the β-Ga₂O₃-based single crystal 36 into a seedcrystal, it is possible to use a technique disclosed in Japanese PatentApplication No. 2013-102599.

Next, an example method of cutting the grown β-Ga₂O₃-based singlecrystal 32 into the β-Ga₂O₃-based single-crystal substrate 1 will bedescribed.

Firstly, the β-Ga₂O₃-based single crystal 32 having a thickness of,e.g., 18 mm is grown and is then annealed to relieve thermal stressduring single crystal growth and to improve electrical characteristics.The annealing is performed e.g., in an inactive atmosphere such asnitrogen while maintaining temperature at 1400 to 1600° C. for 6 to 10hours.

Next, the seed crystal 31 and the β-Ga₂O₃-based single crystal 32 areseparated by cutting with a diamond blade. Firstly, the β-Ga₂O₃-basedsingle crystal 32 is fixed to a carbon stage with heat-melting waxin-between. The β-Ga₂O₃-based single crystal 32 fixed to the stage isset on a cutting machine and is cut for separation. The grit number ofthe blade is preferably about #200 to #600 (defined by JIS B 4131) and acutting rate is preferably about 6 to 10 mm per minute. After cutting,the β-Ga₂O₃-based single crystal 32 is detached from the carbon stage byheating.

Next, the edge of the β-Ga₂O₃-based single crystal 32 is shaped into acircular shape by an ultrasonic machining device or a wire-electricaldischarge machine. Orientation flats may be formed at the edge of thecircularly-shaped β-Ga₂O₃-based single crystal 32.

Next, the circularly-shaped β-Ga₂O₃-based single crystal 32 is sliced toabout 1 mm thick by a multi-wire saw, thereby obtaining theβ-Ga₂O₃-based single-crystal substrate 1. In this process, it ispossible to slice at a desired offset angle. It is preferable to use afixed-abrasive wire saw. A slicing rate is preferably about 0.125 to 0.3mm per minute.

Since the β-Ga₂O₃-based single crystal 32 is a single crystal grown inthe b-axis direction, the principal surface of the β-Ga₂O₃-basedsingle-crystal substrate 1 cut out from the β-Ga₂O₃-based single crystal32 is a plane parallel to the b-axis, such as a (−201) plane, a (101)plane or a (001) plane.

Next, the β-Ga₂O₃-based single-crystal substrate 1 is annealed to reduceprocessing strain and to improve electrical characteristics as well aspermeability. The annealing is performed in an oxygen atmosphere duringtemperature rise and is performed in an inactive atmosphere such asnitrogen atmosphere during when temperature is maintained after thetemperature rise. The temperature to be maintained here is preferably1400 to 1600° C.

Next, the edge of the β-Ga₂O₃-based single-crystal substrate 1 ischamfered (bevel process) at a desired angle.

Next, the β-Ga₂O₃-based single-crystal substrate 1 is ground to adesired thickness by a diamond abrasive grinding wheel. The grit numberof the grinding wheel is preferably about #800 to #1000 (defined by JISB 4131).

Next, the β-Ga₂O₃-based single-crystal substrate is polished to adesired thickness using a turntable and diamond slurry. It is preferableto use a turntable formed of a metal-based or glass-based material. Agrain size of the diamond slurry is preferably about 0.5 μm.

Next, the β-Ga₂O₃-based single-crystal substrate 1 is polished using apolishing cloth and CMP (Chemical Mechanical Polishing) slurry untilatomic-scale flatness is obtained. The polishing cloth formed of nylon,silk fiber or urethane, etc., is preferable. Slurry of colloidal silicais preferably used. The principal surface of the β-Ga₂O₃-basedsingle-crystal substrate 1 after the CMP process has a mean roughness Raof about 0.05 to 0.1 nm.

(Quality Evaluation Method for β-Ga₂O₃-Based Single-Crystal Substrate)

The β-Ga₂O₃-based single-crystal substrate 1 obtained by theabove-mentioned method, etc., is subjected to X-ray rocking curvemeasurement to evaluate crystal quality. The crystal quality isevaluated by evaluating variation in crystal structure of the substratealong the direction parallel to the principal surface as well asperpendicular to the b-axis.

FIG. 4 is a plan view showing the β-Ga₂O₃-based single-crystal substrate1 cut out from the β-Ga₂O₃-based single crystal and X-ray diffractionmeasurement positions thereon. X-ray diffraction intensity is measuredat measurement points shown as “x” in FIG. 4 while rotating thesubstrate about the b-axis of the β-Ga₂O₃-based single crystal, therebyobtaining X-ray rocking curve. These measurement points are aligned on astraight line on the principal surface, which is a line passing throughthe center of the principal surface of the β-Ga₂O₃-based single-crystalsubstrate 1 and perpendicular to the b-axis.

FIG. 5 is a schematic diagram illustrating a state during X-ray rockingcurve measurement. A component of an X-ray emitted from an X-raygenerator 2, when a direction of incidence on the β-Ga₂O₃-basedsingle-crystal substrate 1 (a direction from the X-ray generator 2toward the measurement position on the principal surface of theβ-Ga₂O₃-based single-crystal substrate 1) comes parallel to theprincipal surface of the β-Ga₂O₃-based single-crystal substrate 1,coincides with a straight line on which the measurement points are linedup. FIG. 5 shows, as an example, an incident direction of X-ray whenmeasuring on a straight line which is parallel to a [102] direction andpasses through the center of the (−201)-oriented principal surface ofthe β-Ga₂O₃-based single-crystal substrate 1.

In FIG. 5, ω is an angle [deg] formed by the incident direction of theX-ray and the principal surface of the β-Ga₂O₃-based single-crystalsubstrate 2, and 2θ is an angle formed by the incident direction of theX-ray and a direction from the measurement point toward an X-raydetector 3. To obtain a diffraction peak in X-ray rocking curvemeasurement, ω is changed around an angle satisfying the Bragg'scondition in a state that 2θ is fixed.

This X-ray diffraction measurement was conducted on a non-dopedβ-Ga₂O₃-based single-crystal substrate (referred to as “substrate A”),two β-Ga₂O₃-based single-crystal substrates doped with Sn as a dopant ata charge ratio of 0.030 mol % (referred to as “substrates B and C”) andthree β-Ga₂O₃-based single-crystal substrates doped with Si as a dopantat a charge ratio of 0.020 mol % (referred to as “substrates D, E andF”).

The substrates A, B, C, D and E are substrates cut out from theβ-Ga₂O₃-based single crystals 32 grown in the b-axis direction by usingthe EFG crystal manufacturing apparatus 10 described above, and thesubstrate F is a substrate cut out from the β-Ga₂O₃-based single crystal32 grown by using an apparatus which is basically the same as the EFGcrystal manufacturing apparatus 10 but is not equipped with theafter-heater 20 and the reflective plate 21. The principal surfaces ofthe substrates A, B, C, D and E are the (−201) plane parallel to theb-axis.

FIGS. 6A to 6C and 7A to 7C are graphs showing the curved lines andapproximation lines thereof which represent a relation between themeasurement position on the substrate and an angle ω_(r) [deg]. In FIGS.6A to 6C and 7A to 7C, the horizontal axis indicates a position [mm] onthe substrate in the direction perpendicular to the b-axis, and thevertical axis indicates the angle ω_(r) [deg].

Here, ω_(s) is a value of ω at a peak position of an X-ray rocking curveand ω_(r) is a value obtained by subtracting an average of ω_(s)measured on a straight line from ω_(s). ω_(r) is indicated on thevertical axis in FIGS. 6 and 7 since each graph is standardized suchthat the average value of ω_(s) in becomes 0°, and it is thus easy tocompare the graphs.

FIGS. 6A, 6B and 6C are graphs respectively showing the measurementresults of the substrates A, B and C. FIGS. 7A, 7B and 7C are graphsrespectively showing the measurement results of the substrates D, E andF. The diffraction peaks of X-ray rocking curve in FIGS. 6A to 6C and 7Ato 7C are from a (−402) plane.

Based on FIGS. 6A to 6C and 7A to 7C, an angle on a straightapproximation line (hereinafter, referred to as ω_(a)) is subtractedfrom the angle ω_(r) at each measurement position, and a difference Δω[deg] between the maximum value and the minimum value of the obtainedvalue is calculated. Also, the angle ω_(a) is subtracted from the angleω_(r) at each measurement position, and the average α [deg] of absolutevalues of the obtained values is calculated. To obtain the approximationline, the curved line representing a relation between the measurementposition and the angle ω_(r) is linearly approximated using the leastsquares method.

Δω also can be obtained by using ω_(s) instead of using ω_(r). In otherwords, the approximation line of the curved line representing a relationbetween ω_(s) and the measurement position is obtained by linearapproximation using the least squares method, the angle ω_(a) on theapproximation line is subtracted from ω_(s) at each measurementposition, and Δω is obtained as a difference between the maximum valueand the minimum value of the value obtained by the subtraction.Obviously, the value of Δω is the same either with ω_(r) or with ω_(s).Likewise, α can be obtained by using ω_(s) instead of ω_(r).

The smaller the variation in the angle ω_(r) in a directionperpendicular to the b-axis, the smaller the values of Δω and α, andthus the smaller the variation in crystal structure of the substratealong the direction perpendicular to the b-axis.

Plural β-Ga₂O₃-based single-crystal substrates doped with Sn as a dopantwere cut out from the β-Ga₂O₃-based single crystal 32 grown by the EFGcrystal manufacturing apparatus 10, and x-ray diffraction was alsoconducted on substrates other than the substrates B and C. The substrateC had the largest Δω and α among all substrates including the substratesB and C.

Meanwhile, plural β-Ga₂O₃ single-crystal substrates doped with Si as adopant were cut out from the β-Ga₂O₃-based single crystal 32 grown bythe EFG crystal manufacturing apparatus 10, and x-ray diffraction wasalso conducted on substrates other than the substrates D and E. Thesubstrate E had the largest Δω and α among all substrates including thesubstrates D and E.

The numerical values of the Δω and α of each substrate are shown inTable 1 below.

TABLE 1 After-heater and Substrate Dopant Reflective plate Δω [deg] α[deg] A — With 0.0215 0.005 B Sn With 0.0212 0.007 C Sn With 0.45400.119 D Si With 0.0473 0.011 E Si With 0.7264 0.141 F Si Without 1.15690.283

Although the principal surface of the substrates A, B, C, D, E and F arethe (−201) plane as described above, similar Δω and α are obtained fromother planes such as (101) or (001) plane as long as it is parallel tothe b-axis.

Group IV elements such as Sn, Si, Ge and Pb are elements suitable as ann-type dopant for β-Ga₂O₃-based single crystals. When Ge or Pb, whichare Group IV elements and not shown in Table 1, is used as a dopant,variation in crystal structure (Δω and α) of the β-Ga₂O₃-basedsingle-crystal substrate is substantially the same as when using Si.

The values of Δω and α of the substrates A, B, C, D and E arerespectively not more than 0.7264 and not more than 0.141, and aresmaller than those of the substrate F. This is because the substrates A,B, C, D and E are cut out from the β-Ga₂O₃-based single crystal 32 grownby the EFG crystal manufacturing apparatus 10 which is equipped with theafter-heater 20 and the reflective plate 21.

The substrates A, B, C, D and E are substrates cut out from theβ-Ga₂O₃-based single crystal 32 grown in the b-axis direction.Therefore, the values of Δω and α on a straight line located on theprincipal surface and perpendicular to the b-axis coincident with thegrowth direction of the β-Ga₂O₃-based single crystal 32 are the largestamong Δω and α on any straight lines (all straight lines) on theprincipal surfaces of the substrates A, B, C, D and E. In other words,when Δω and α on, e.g., a straight line perpendicular to the b-axis arerespectively not more than 0.7264 and not more than 0.141, the maximumvalues of Δω and α on a given straight line are respectively not morethan 0.7264 and not more than 0.141.

Change in Δω and α caused by warpage of substrate was evaluated. Theresult is as follows. Δω and α are parameters obtained from inclinationof crystal lattice of each portion on the substrate surface, and arethus affected also by warpage of substrate in addition to variation incrystal structure of the substrate. This evaluation is conducted todemonstrate that change in Δω and α caused by warpage of substrate iswell smaller than change in Δω and α caused by variation in crystalstructure and does not affect the evaluation of variation in crystalstructure using the values of Δω and α.

Firstly, five substrates having a (−201)-oriented principal surfaces anddoped with Sn as a dopant at a charge ratio of 0.10 mol % (referred toas “substrates G, H, I, J and K”) are cut out from the β-Ga₂O₃-basedsingle crystal 32 grown by using the EFG crystal manufacturing apparatus10, and height of the surface is measured at each position on thesubstrate surface. Values of “Bow” and “Warp”, which are indications oflevel of warpage of substrate, are obtained from data of the height ofsurface at each position.

Next, based on the data of the height of surface at each position on thesubstrate surface, an inclination θ at each position on the substratesurface is calculated. The inclination θ causes the angle ω in X-rayrocking curve to be shifted (by θ°). Δω and α affected by warpage ofsubstrate can be obtained based on the inclination θ at each position onthe substrate surface.

Table 2 below shows the numerical values of Bow and Warp indicating thelevel of warpage of the substrates G, H, I, J and K, and also shows thenumerical values, affected by warpage of each substrate, of Δω and α ona straight line which is located on the principal surface, passesthrough the center of the principal surface of the substrate and isperpendicular to the b-axis.

TABLE 2 Substrate Δω [deg] α [deg] Bow [μm] Warp [μm] G 0.0540 0.002−9.479 15.704 H 0.0551 0.002 −12.933 24.805 I 0.0471 0.003 −11.23922.462 J 0.0469 0.003 −10.905 18.758 K 0.0595 0.003 −10.838 14.451

As shown in Table 2, the numerical values of Δω and α affected bywarpage of substrate are well smaller than the change in Δω and α causedby variation in crystal structure shown in Table 1, and substantially donot have an impact on the evaluation of variation in crystal structureusing the values of Δω and α. Such warpage level of substrate which iscut out from the β-Ga₂O₃-based single crystal 32 substantially does notdepend on the presence of dopant or the type of dopant.

Effects of the Embodiment

According to the present embodiment, it is possible to obtain ahigh-quality β-Ga₂O₃-based single-crystal substrate having little smallvariation in crystal structure even when a dopant is added.

Although the embodiment of the invention has been described, theinvention is not intended to be limited to the embodiment, and thevarious kinds of modifications can be implemented without departing fromthe gist of the invention.

In addition, the invention according to claims is not to be limited tothe embodiment described above. Further, it should be noted that allcombinations of the features described in the embodiment are notnecessary to solve the problem of the invention.

INDUSTRIAL APPLICABILITY

A high-quality β-Ga₂O₃-based single-crystal substrate having littlevariation in crystal structure is provided.

REFERENCE SIGNS LIST

-   1: β-Ga₂O₃-based single crystal substrate-   32: β-Ga₂O₃-based single crystal-   113: lid

The invention claimed is:
 1. A β-Ga₂O₃-based single-crystal substrate,comprising: a β-Ga₂O₃-based single crystal; and a principal surfacebeing a plane parallel to a b-axis of the β-Ga₂O₃-based single crystal,wherein the maximum value of Δω on an arbitrary straight line on theprincipal surface that passes through the center of the principalsurface is not more than 0.7264, and wherein the Δω is the differencebetween the maximum value and the minimum value of values obtained bysubtracting ωa from ωs at each of measurement positions, where ωsrepresents an angle defined by an X-ray incident direction and theprincipal surface at a peak position of an X-ray rocking curve on thestraight line and ωa represents an angle on an approximated straightline obtained by using least-squares method to linearly approximate acurve representing a relationship between the ωs and the measurementpositions thereof, wherein the β-Ga₂O₃-based single-crystal substratecomprises a dopant, wherein the dopant is a Group IV element.
 2. Aβ-Ga₂O₃-based single-crystal substrate, comprising: a β-Ga₂O₃-basedsingle crystal; and a principal surface being a plane parallel to ab-axis of the β-Ga₂O₃-based single crystal, wherein the maximum value ofα on an arbitrary straight line on the principal surface that passesthrough the center of the principal surface is not more than 0.141, andwherein the α is an average value of absolute values obtained bysubtracting ωa from ωs at each of measurement positions, where ωsrepresents an angle defined by an X-ray incident direction and theprincipal surface at a peak position of an X-ray rocking curve on thestraight line and ωa represents an angle on an approximated straightline obtained by using least-squares method to linearly approximate acurve representing a relationship between the ωs and the measurementpositions thereof, wherein the β-Ga₂O₃-based single-crystal substratecomprises a dopant, wherein the dopant is a Group IV element.
 3. Theβ-Ga₂O₃-based single-crystal substrate according to claim 1, wherein Δωon a straight line perpendicular to the b-axis of the β-Ga₂O₃-basedsingle crystal is a maximum among the Δω on the arbitrary straight line.4. The β-Ga₂O₃-based single-crystal substrate according to claim 2,wherein α on a straight line perpendicular to the b-axis of theβ-Ga₂O₃-based single crystal is a maximum among the α on the arbitrarystraight line.
 5. The β-Ga₂O₃-based single-crystal substrate accordingto claim 1, wherein the dopant is Sn or Si.
 6. The β-Ga₂O₃-basedsingle-crystal substrate according to claim 1, wherein the principalsurface is a (−201) plane, a (101) plane or a (001) plane.
 7. Theβ-Ga₂O₃-based single-crystal substrate according to claim 1, wherein thesubstrate is cut out from a flat-plate-shaped β-Ga₂O₃-based singlecrystal grown in the b-axis direction.
 8. The β-Ga₂O₃-basedsingle-crystal substrate according to claim 1, wherein the substratecomprises no twinning plane or a region that does not include a twinningplane that is not less than 2 inches in a maximum width in a directionperpendicular to an intersection line between the twinning plane and theprincipal surface.